Question

what is the total displacement over the time interval of 0-7 seconds?

Explanation:

Step1: Identify the method

The displacement is the area under the velocity - time graph.

Step2: Divide the graph into shapes

The graph can be divided into a rectangle from \(t = 0\) to \(t = 5\) and a trapezoid from \(t=5\) to \(t = 7\).

Step3: Calculate the area of the rectangle

The rectangle has a height \(v = 6\ m/s\) and base \(b = 5\ s\). The area of the rectangle \(A_1=v\times t=6\times5 = 30\ m\).

Step4: Calculate the area of the trapezoid

The trapezoid has bases \(b_1 = 6\ m/s\) and \(b_2=4\ m/s\) and height \(h = 2\ s\). The area of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\), so \(A_2=\frac{(6 + 4)\times2}{2}=10\ m\).

Step5: Calculate the total displacement

The total displacement \(d=A_1+A_2=30 + 10=40\ m\).

Answer:

\(40\ m\)